The unique group of Order 3. It is both Abelian and Cyclic. Examples include the Point Groups and and the integers under addition modulo 3. The elements of the group satisfy where 1 is the Identity Element. The Cycle Graph is shown above, and the Multiplication Table is given below.

1 | |||

1 | 1 | ||

1 | |||

1 |

The Conjugacy Classes are , ,

and ,

The irreducible representation (Character Table) is therefore

1 | |||

1 | 1 | 1 | |

1 | 1 | ||

1 | 1 |

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1999-05-26